Question: Suppose that in a large population the proportion of people that have a certain disease is 0.01. Use the Poisson approximation to the binomial distribution to find the probability that in a random group of 200 people at least four people will have the disease. The probability is ?
2. Suppose that one word is to be selected at random from the sentence THE GIRL PUT ON HER BEAUTIFUL RED HAT. If X denotes the number of letters in the word that is selected, what is the value of Var(X 2)? Edit
Answer: 1. p=0.01 and n=200
According to poission distribution, P(X=r)=e^(-mu)mu^r/r!
var(X)=Σx^2/n - (Σx/n)^2=18.25-14.06=4.19(Ans.) Edit
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